Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
The fractional ratio indicates that for every 3 Republicans, there are 5 Democrats, a ratio of 3 : 5. We first set up this ratio of registered Republicans to registered Democrats using a variable multiplier:
Republicans: Democrats = 3x : 5x
We are given that 600 additional Republicans and 500 additional Democrats registered and that the new ratio of Republicans to Democrats was 4 to 5. This means that the new number of Republicans can be expressed as (3x + 600), and the new number of Democrats can be expressed as (5x + 500). We can put all this into an equation:
R/D –> (3x+600)/(5x+500) = 4/5
After cross multiplying we have:
5(3x+600) = 4(5x+500)
15x + 3,000 = 20x + 2,000
1,000 = 5x
x = 200
Thus after the registration we have the following:
Democrats = (5 × 200) + 500 = 1,500
Republicans = (3 × 200) + 600 = 1,200
There are 1,500 – 1,200 = 300 more Democrats than Republicans.
Answer: B
